Shedding Light on Solid Sorbents: Evaluation of Supported Potassium Carbonate Particle Size and Its Effect on CO2 Capture from Air

Solid sorbents are essential for developing technologies that directly capture CO2 from air. In solid sorbents, metal oxides and/or alkali metal carbonates such as potassium carbonate (K2CO3) are promising active components owing to their high thermal stability, low cost, and ability to chemisorb the CO2 present at low concentrations in air. However, this chemisorption process is likely limited by internal diffusion of CO2 into the bulk of K2CO3. Therefore, the size of the K2CO3 particles is expected to be an important factor in determining the kinetics of the sorption process during CO2 capture. To date, the effects of particle size on supported K2CO3 sorbents are unknown mainly because particle sizes cannot be unambiguously determined. Here, we show that by using a series of techniques, the size of supported K2CO3 particles can be established. We prepared size-tuned carbon-supported K2CO3 particles by tuning the K2CO3 loading. We further used melting point depression of K2CO3 particles to collectively estimate the average K2CO3 particle sizes. Using these obtained average particle sizes, we show that the particle size critically affects the efficiency of the sorbent in CO2 capture from air and directly affects the kinetics of CO2 sorption as well as the energy input needed for the desorption step. By evaluating the mechanisms involved in the diffusion of CO2 and H2O into K2CO3 particles, we relate the microscopic characteristics of sorbents to their macroscopic performance, which is of interest for industrial-scale CO2 capture from air.

* harry.bitter@wur.nl, nazila.masoud@wur.nl Table of -desorption isotherms for KetjenBlack support, KB10, KB25, and KB50 were measured to establish textural properties of the samples and support indicate the presence of potassium, but extraction of an average particle size was not possible.

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Note that background potassium is zero: SEM images and EDX mapping of the sample and an area on the sample holder. It shows that on the sample holder there is no background potassium. Figure S.3. TEM images of one K 2 CO 3 particle captured over time. Sample (KB50) was exposed to beam (a). Images on the same particle were captured in sequence of 10 seconds (b, c, and d). Images show fast changes of the K 2 CO 3 under the beam. The K 2 CO 3 particles disappeared under the beam if the image is not captured fast enough.

Quantitative XPS analysis
We used a model developed by Kerkhof and Moulijn 1 to estimate K 2 CO 3 particle sizes for KB10, KB25, and KB50.
The model suggests that a relative XPS intensity ratio sourced from an element from a metal or metal oxide to an element from a high surface area support relates to the dispersion of the metal/metal oxide on the support. The model assumes that the sample consists of sheets of support with cubic particles of the promoter (here we consider cubes of K 2 CO 3 particles) with size of c in between support sheets (Scheme 1.a).
The thickness of the support sheets, t, is calculated as where ρ s is support density (carbon: 2.0 g/cm 3 Where A is the effective area of the sample from which electrons reach the detector; the atomic densities in promoter and support (n p , n s ); the photoelectron cross sections (σ s , σ p ); the escape depths of the electrons (λ); and f is the fraction of support covered with promoter that follows: Here, x is the promoter weight fraction in the sample.
Further, the total amount of escaping electrons from an infinite number of sheets is summed up considering that the most contribution to the signal is from the top layers. Samples with high surface area support like the KB series sorbents are assumed to have an infinite number of sheets. Hence, we use the model suggesting following equation for the experimentally obtained relative XPS intensities of promoter and support, (I p /I s ) exp . In our case, (I p /I s ) exp is the relative XPS Scheme S.1. a) Schematic presentation of the sample described in the model and b) Supported K 2 CO 3 particles on carbon: invisible and visible by XPS. In principal, the thickness of the blue layer should change because only perpendicular emission is assumed. Nevertheless, due to large size of particles compared to the penetration depth, this correction was waived.
intensities of potassium (K 2p) to carbon from support (C 1s, sp 2 ), and they are experimentally obtained from the high resolution K 2p and C 1s XP spectra of the samples ( Figure S.3 D is detector efficiency as a function of the kinetic energy of the electrons. P is fraction of the electrons from one layer of promoter or support passing through another layer of promoter or support. The fraction of electrons from one support layer passing through a layer of support is P ss , and the fraction from one layer of promoter passing through a layer of support P ps and etc. They are functions of particle size, support thickness and support coverage (f): Where dimensionless particle sizes are defined as: And dimensionless support thickness are defined as:  We try to simplify the formula to have a direct relation of the particle size to the experimentally obtained relative XPS intensities.
First, we assumed for our samples P sp ≈ P pp ≈ 1. It seems a valid assumption when f, coverage of support by the promoter, is negligible. We examined the validity of this assumption for two extreme cases of K 2 CO 3 loadings and particle sizes on carbon considering support surface area is not lost during K 2 CO 3 deposition: Hence the formula simplifies to: By substituting I p,0 , I s,0 , and the bulk atomic ratio of the support and the promoter (p/s) b : the equation is elaborated to:

The equation is reduced to
Here, α 1 contains particle size information and is obtained as follows.
For a hypothetical monolayer of promoter on the support, α is small and (1 -exp(-α 1 ))/α 1 goes to 1. Hence hypothetical (I p /I s ) monolayer is equal to (p/s) b (σ p /σ s ) and needs to be calculated for KB50, KB25, and KB10 samples. The bulk atomic ratio of the support and the promoter (p/s) b is known for these three samples (

α1
(1-exp(-α1))/α1   Figure S.7). This reaction and the heat flow associated with that eclipsed the melting of the K₂CO₃.  More water content of the flow led to a more calculated CO₂ uptake. We suspect that the CO₂ uptake measured by TGA is subject to error due to interfering water uptake that overestimates the CO₂ uptake. On the other hand, water concentration may affect the sorption of CO 2 and/or water. These two effects are not easily distinguishable. Hence kinetics reported under TGA condition is not representative of the kinetics of the reaction in a flow reactor.  The enthalpy of decarbonation was calculated as 120 kJ/mol. It is more than reported value of 107 kJ/mol. 5 CO₂ uptake was also more than 1 mol/mol K₂CO₃. It means part of the mass loss is due to dehydration instead of decarbonation.

Details of the calculation of the apparent activation energy for decarbonation steps
Redhead analysis 6 provides a simple way for the estimation of apparent activation energies for a first order desorption step in a typical temperature programmed desorption measurement. The analysis is based on Arrhenius equation and assumes the apparent activation energy of desorption (E d ) and pre-exponential factor (A) are coverage independent.
The analysis suggests the following equation to relate the heating rate ( ) to the temperature that a maximum desorption peak (T p ) appears, Where R is the gas constant. By rearranging the formula the following is obtained,